Discontinuous modelling of masonry failure

Abstract

A robust and efficient numerical model is a valuable engineering tool for predicting the load-bearing capacity and failure mode of masonry structures. Such a computational model consists of three key ingredients: a constitutive law which incorporates the non-linear material responses, a kinematic framework for describing failure mechanisms, and a solution algorithm which is capable of modelling the complete loading behaviour of a structure up to total failure. This work focuses on the latter two aspects by presenting three discontinuous masonry models and a novel non-incremental solution algorithm. The proposed mesoscopic masonry models allow the modelling of accurate crack paths since mortar joints and bricks are modelled as separate entities. The kinematics of these masonry constituents are described by the partition of unity finite element method, extending the capabilities of conventional finite element-based masonry models. In the first masonry model, the joint thickness is explicitly modelled and embedded within the finite element mesh. This is in contrast with the second masonry model, in which joints are represented by zero-thickness interfaces positioned at the finite element edges. Although this model has strong analogies with classical finite element-based mesoscale masonry models, the partition of unity framework offers new possibilities for the improvement of the model efficiency, such as element- embedment of discontinuities and their introduction during the computation. The latter methodology is applied in the third masonry model, in which joints are only introduced if a critical stress state is exceeded in the material. In the second part of this work, a novel solution algorithm is proposed for modelling non-linear behaviour of masonry and other quasi-brittle materials. The algorithm belongs to the class of non-incremental LArge Time INcrement (LATIN) methods, in which the whole loading process is iteratively calculated in one single time increment. At variance with existing LATIN methods, the proposed algorithm is capable of tracing snap-backs, i.e. a decrease of both stress and strain under loading. This phenomenon is commonly observed in the mechanical responses of masonry structures and other quasi-brittle materials. Finally, the performance and objectivity of these modelling strategies and tools is examined through several case studies in which a comparison is made with experimental data from literature. It is shown that the developed computational framework is capable of predicting realistic crack patterns and peak loads.